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Solving Schrödinger Bridges via Maximum Likelihood

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The Computer Laboratory, Department of Computer Science and Technology, University of Cambridge, William Gates Building, 15 JJ Thomson Avenue, Cambridge CB3 0FD, UK
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The Cavendish Laboratory, Deparment of Physics, The Old Schools, Trinity Ln, Cambridge CB2 1TN, UK
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Authors to whom correspondence should be addressed.
Academic Editor: Sotiris Kotsiantis
Entropy 2021, 23(9), 1134; https://doi.org/10.3390/e23091134
Received: 21 July 2021 / Revised: 11 August 2021 / Accepted: 23 August 2021 / Published: 31 August 2021
The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. Our main contribution is the proof of equivalence between solving the SBP and an autoregressive maximum likelihood estimation objective. This formulation circumvents many of the challenges of density estimation and enables direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments. View Full-Text
Keywords: Schrödinger bridges; machine learning; stochastic control Schrödinger bridges; machine learning; stochastic control
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MDPI and ACS Style

Vargas, F.; Thodoroff, P.; Lamacraft, A.; Lawrence, N. Solving Schrödinger Bridges via Maximum Likelihood. Entropy 2021, 23, 1134. https://doi.org/10.3390/e23091134

AMA Style

Vargas F, Thodoroff P, Lamacraft A, Lawrence N. Solving Schrödinger Bridges via Maximum Likelihood. Entropy. 2021; 23(9):1134. https://doi.org/10.3390/e23091134

Chicago/Turabian Style

Vargas, Francisco, Pierre Thodoroff, Austen Lamacraft, and Neil Lawrence. 2021. "Solving Schrödinger Bridges via Maximum Likelihood" Entropy 23, no. 9: 1134. https://doi.org/10.3390/e23091134

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